An Asymmetric Extension for the Family of Elliptical Slash Distributions

In this article, we introduce an asymmetric extension to the univariate slash-elliptical family of distributions studied in Gomez et al. (2007a). This new family results from a scale mixture between the epsilon-skew-symmetric family of distributions and the uniform distribution. A general expression is presented for the density with special cases such as the normal, Cauchy, Student-t, and Pearson type II distributions. Some special properties and moments are also investigated. Results of two real data sets applications are also reported, illustrating the fact that the family introduced can be useful in practice.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

Quantum exchange interaction of spherically symmetric plasmoids

We study nano-sized spherically symmetric plasma structures which are radial nonlinear oscillations of electrons in plasma. The effective interaction of these plasmoids via quantum exchange forces between ions is described. We calculate the energy of this interaction for the case of a dense plasma. The conditions when the exchange interaction is attractive are examined and it is shown that separate plasmoids can form a single object. The application of our results to the theoretical description of stable atmospheric plasma structures is considered. (C) 2012 Elsevier Ltd. All rights reserved.

Local power properties of some asymptotic tests in symmetric linear regression models

In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of symmetric linear regression models. This is a wide class of models which encompasses the t model and several other symmetric distributions with longer-than normal tails. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2011 Elsevier B.V. All rights reserved.

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

Gastric Torsion from an Intestinal Hernia Through a Rent in the Gastrosplenic Ligament in a Horse

The present report describes an 8-year-old gelding presenting with signs of severe abdominal pain. After performing a thorough physical examination, including rectal palpation and additional diagnostic tests, an exploratory laparotomy was recommended. The jejunum was found herniated through the gastrosplenic ligament, and the stomach was severely distended with gas. Given a poor prognosis, the horse was euthanized on the table. At necropsy, the stomach appeared dilated, with an 180 horizontal gastric torsion, from left (lateral) to right (medial), dividing the organ into dorsal and ventral compartments. We believe that the chronic traction exerted by an incarcerated and distended loop of jejunum, in the dorsal aspect of the gastrosplenic ligament, associated with trauma during episodes of intense rolling, enlarged the rent until it ruptured. Because of this rupture, the lateral dorsal aspect of the stomach became unattached, predisposing it to the torsion. (C) 2012 Elsevier Inc. All rights reserved.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

Mixed-valence state of symmetric diruthenium complexes: synthesis, characterization, and electron transfer investigation

Complexes of the type {[(pyS)Ru(NH3)(4)](2)-mu-L}(n), where pyS = 4-mercaptopyridine, L = 4,4'-dithiodipyridine (pySSpy), pyrazine (pz) and 1,4-dicyanobenzene (DCB), and n = +4 and +5 for fully reduced and mixed-valence complexes, respectively, were synthesized and characterized. Electrochemical data showed that there is electron communication between the metal centers with comproportionation constants of 33.2, 1.30 x 10(8) and 5.56 x 10(5) for L = pySSpy, pz and DCB, respectively. It was also observed that the electronic coupling between the metal centers is affected by the p-back-bonding interaction toward the pyS ligand. Raman spectroscopy showed a dependence of the intensity of the vibrational modes on the exciting radiations giving support to the assignments of the electronic transitions. The degree of electron communication between the metal centers through the bridging ligands suggests that these systems can be molecular wire materials.

Shear force and torsion in reinforced concrete beam elements: theoretical analysis based on Brazilian Standard Code ABNT NBR 6118:2007

Reinforced concrete beam elements are submitted to applicable loads along their life cycle that cause shear and torsion. These elements may be subject to only shear, pure torsion or both, torsion and shear combined. The Brazilian Standard Code ABNT NBR 6118:2007 [1] fixes conditions to calculate the transverse reinforcement area in beam reinforced concrete elements, using two design models, based on the strut and tie analogy model, first studied by Mörsch [2]. The strut angle θ (theta) can be considered constant and equal to 45º (Model I), or varying between 30º and 45º (Model II). In the case of transversal ties (stirrups), the variation of angle α (alpha) is between 45º and 90º. When the equilibrium torsion is required, a resistant model based on space truss with hollow section is considered. The space truss admits an inclination angle θ between 30º and 45º, in accordance with beam elements subjected to shear. This paper presents a theoretical study of models I and II for combined shear and torsion, in which ranges the geometry and intensity of action in reinforced concrete beams, aimed to verify the consumption of transverse reinforcement in accordance with the calculation model adopted As the strut angle on model II ranges from 30º to 45º, transverse reinforcement area (Asw) decreases, and total reinforcement area, which includes longitudinal torsion reinforcement (Asℓ), increases. It appears that, when considering model II with strut angle above 40º, under shear only, transverse reinforcement area increases 22% compared to values obtained using model I.

Width of buccal and posterior corridors: differences between cases treated with asymmetric and symmetric extractions

OBJECTIVE: To verify if there is difference in the buccal and posterior corridor width in cases treated with extraction of one and four premolars. METHODS: Through posed smile photographs of 23 Class II patients, subdivision, treated with extraction of one premolar and 25 Class I and Class II patients, subdivision, treated with extraction of four premolars, the percentage of buccal and posterior corridor width was calculated. The two protocols of extractions were compared regarding the buccal and posterior corridor width by independent t tests. RESULTS: There was no statistically significant difference on the buccal and posterior corridor widths between patients treated with symmetric and asymmetric extraction. CONCLUSION: The buccal and posterior corridor did not differ between the evaluated protocols of extractions.

Structural stability of flexible lines in catenary configuration under torsion

Catenary risers can present during installation a very low tension close to seabed, which combined with torsion moment can lead to a structural instability, resulting in a loop. This is undesirable once it is possible that the loop turns into a kink, creating damage. This work presents a numerical methodology to analyze the conditions of loop formation in catenary risers. Stability criteria were applied to finite element models, including geometric nonlinearities and contact constraint due to riser-seabed interaction. The classical Greenhill's formula was used to predict the phenomenon and parametric analysis shows a “universal plot” able to predict instability in catenaries using a simple equation that can be applied for typical risers installation conditions and, generically, for catenary lines under torsion.

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.